Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#6432 | C2 | semidirect |
| 4. #89779 | C2 | direct (N × H) |
| 5. C2×#6381 | C2 | semidirect |
| 6. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 19. #6432 | C22 | semidirect |
| 21. #6381 | C22 | semidirect |
| 22. C4⋊(C7⋊C8) | C22 | semidirect |
| 27. C2×C7×D4 | Q8 | semidirect |
| 61. C7×D4 | C2×Q8 | semidirect |
| 113. C2×D4 | Dic14 | semidirect |
| 133. C2×C7 | #474 | semidirect |
| 145. D4 | C2×Dic14 | semidirect |
| 160. C7 | C2×#474 | semidirect |
| 177. C2 | #89779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C2×#6432 | 2 |
| C2×#6406 | 2 |
| #89779 | 2 |
| C2×#6381 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C2×#474 | 7 |